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Decomposition of group into a maximal subgroup and commutation relations between generators

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#group-theory #lie-groups #lie-algebras #mathematical-physics
99
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$\nabla_{\tilde{X}} (\tilde{X})=0$ for all $X \in g$ implies $g(\tilde{Z}, [\tilde{X}, \tilde{Z}])=0$

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#lie-groups #riemannian-geometry #lie-algebras
255
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showing $\exp : \mathfrak{gl}(n, \mathbb{C}) \rightarrow GL(n,\mathbb{C})$ is surjective.

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#lie-groups #lie-algebras
66
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Tits' field of 1 element philosophy for $G_2$

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#lie-groups #finite-fields #algebraic-groups
534
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Gauge transformation as Lie Group

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#lie-groups #gauge-theory
204
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Expression of element in lie algebra, $sp(p,q)$

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#lie-groups #lie-algebras
25
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Compute $e^{ t( 2 x \frac{d}{dx} + 3 y \frac{d}{dy})} f(x,y)$

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#ordinary-differential-equations #multivariable-calculus #lie-groups
669
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Connected component of identity and normal subgroups

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#lie-groups #connectedness #normal-subgroups #path-connected
825
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Fundamental group of topological product space

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#algebraic-topology #lie-groups #fundamental-groups
147
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Humphreys page 63 - error?

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#representation-theory #lie-groups #algebraic-groups
167
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Universal covering group of a semidirect product of Lie groups

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#lie-groups #covering-spaces #fundamental-groups #semidirect-product
101
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Not all homogeneous manifolds are on the form $G/H$

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#differential-geometry #lie-groups #riemannian-geometry
140
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Unitary matrix map is continuous

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#linear-algebra #general-topology #matrices #continuity #lie-groups
174
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How to show that $\mathbb{C}[SL_n]^N$ is generated by flag minors?

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#commutative-algebra #lie-groups #algebraic-groups
1.2k
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How can we describe the Lie algebra of PGL(n)?

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#lie-groups #lie-algebras

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